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 A348067 Matula-Goebel tree number of tree n with a new leaf added below each existing vertex. 2
 2, 6, 26, 18, 202, 78, 122, 54, 338, 606, 2462, 234, 794, 366, 2626, 162, 1346, 1014, 502, 1818, 1586, 7386, 4546, 702, 20402, 2382, 4394, 1098, 8914, 7878, 43954, 486, 32006, 4038, 12322, 3042, 2962, 1506, 10322, 5454, 12178, 4758, 4946, 22158, 34138, 13638 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS k times nested a(a(...a(1))) = A076146(k+1) is the Matula-Goebel number of the binomial tree order k constructed by an "expansion" method starting from a singleton and successively adding a new leaf under every vertex. LINKS Kevin Ryde, Table of n, a(n) for n = 1..5000 FORMULA a(n) = 2 * Product_{i=1..k} prime(a(primepi(p[i]))), where n = p[1]*...*p[k] is the prime factorization of n with multiplicity (A027746). EXAMPLE tree n=6   tree a(6) = 78   R             R___        root R   | \           |\  \   A  B          A @  B      new vertices   |             |\    \     "@" below each   C             C @    @    existing                  \                   @ PROG (PARI) a(n) = my(f=factor(n)); 2*factorback([prime(self()(primepi(p))) | p<-f[, 1]], f[, 2]); CROSSREFS Cf. A027746 (prime factors), A076146 (binomial tree). Cf. A297002 (add leaves under children of the root). Sequence in context: A178087 A109286 A009466 * A032479 A029988 A050573 Adjacent sequences:  A348064 A348065 A348066 * A348068 A348069 A348070 KEYWORD nonn AUTHOR Kevin Ryde, Oct 01 2021 STATUS approved

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Last modified June 26 00:12 EDT 2022. Contains 354870 sequences. (Running on oeis4.)